title: Directional edge enhancement in optical tomography of thin phase objects.
abstract: In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projection data leaving the slice of a thin phase object. These modified projections are stacked in such a way that they form a modified sinogram called Hilbert-sinogram. We prove that the inverse Radon-transform of this sinogram is the directional Hilbert-transform of the slice function, and the reconstructed image is the directional edge enhancement of the distribution function on the slice. The Hilbert-transform is implemented by a 4f optical Fourier-transform correlator and a spatial filter consisting of a phase step of π radians. One important feature of this proposal is to perform a turn of 180° in the spatial filter at a certain value of the projection angle within the range [0°, 360°]. The desired direction of enhancement can be chosen by the proper selection of such turning angle. We present both the mathematical modeling and numerical results.
authors.affiliation: Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico-Matemáticas, Posgrado en Física Aplicada, Apdo. Postal 1152, CP 72570 Puebla, Pue. México. cmeneses@fcfm.buap.mx
authors.forename: Cruz
authors.initials: C
authors.lastname: Meneses-Fabian
authors.forename: Areli
authors.initials: A
authors.lastname: Montes-Perez
authors.forename: Gustavo
authors.initials: G
authors.lastname: Rodriguez-Zurita
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D041622:Tomography, Optical / Q000379:methods*